1 Introduction

The manifold ecological and societal benefits urban trees provide (e.g., Roy et al., 2012) depend critically on their health and performance. For instance, trees alter local energy budgets (Grimmond et al., 1996 ; Hertel and Schlink, 2019) through shading and transpiration (Endlicher et al., 2016; Gillner et al., 2015), and therefore can reduce ambient temperatures, infrastructure power-consumption and (human) thermal discomfort (Akbari et al., 2001; e.g. Gulyás et al., 2006; Hoyano, 1988; Mayer and Höppe, 1987). However, excess heat common for cities (i.e., Urban Heat Island, UHI, Oke, 1982), combined with other urban conditions, affects tree physiological functioning with outcomes ranging from enhanced growth to early senescence, branch die-back, and even mortality (Au, 2018; Gillner et al., 2014; e.g., Hilbert et al., 2019). Thus, assessing the effect of increased temperatures on trees, as part of urban green infrastructure, is instrumental for understanding as well as adapting to current and expected conditions in this century (Ward and Johnson, 2007), especially considering ever more urbanized societies and the potential for UHI effects to compound with more frequent atmospheric drought (Brune, 2016; Norton et al., 2015; Roloff et al., 2009).

The UHI effect, i.e., the difference between urban and adjacent rural (air) temperatures, has been intensively studied for several decades (cf. Oke, 1982; Stewart, 2011). It is typically related to the structure and density of urban land-use (Kuttler et al., 2015), which can be characterized through local climate zones, and modulated by physiographic and urban characteristics, such as vicinity to water bodies, predominant wind and street direction, etc. (Stewart and Oke, 2012); yet, the physical basis for the excess heat in cities is to a large extent found in the altered surface energy balance as the proportional cover of vegetation decreases compared to rural (or reference) systems (Hertel and Schlink, 2019; Oke, 1992). In temperate climates, this results in strongest UHI magnitudes at night (cf. Fenner et al., 2014). For example, Berlin features the most intense UHI in Germany due to its large extent and development intensity with an average air temperature increase of around 5 K at night-times (2001-2010) with maxima of up to 11 K (Fenner et al., 2014) in urban \(vs.\) rural areas.

Increased air temperatures due to UHIs can affect tree growth through altering several physiological processes across plant organs directly or indirectly (Dusenge et al., 2019). Generally, reaction times at cellular level increase with temperature up to a maximum, after which a drop in enzymatic activity results in a species-dependent optimum curve (Arcus et al., 2016; Parent et al., 2010). In leaves this optimum response is reflected in the net assimilation rate of carbohydrates, as a balance of photosynthesis and respiration, with losses exceeding gains more rapidly with increasing temperatures (Long, 1991). These responses vary between species (Tjoelker et al., 2001) as well as intra-specifically due to local acclimation, i.e., a shift of optimum temperature responses after prolonged exposure (Yamori et al., 2014), and threshold temperatures before tissue damage occurs (for review see Geange et al., 2021). High temperatures in temperate areas are often coincident with low relative air humidity (i.e., large vapor pressure deficit), which in turn can decrease stomatal conductance governing the majority of gas exchange in leaves (Grossiord et al., 2020), and thus the capacity for photosynthesis. Under prolonged stomatal closure (or decreased conductance) with high temperatures, trees may thus face decreased growth (in subsequent years) or even starvation as their carbohydrate reserves are depleted yet not replenished at sufficient rates (McDowell et al., 2008). Furthermore, air (and soil temperatures) affect the initiation, speed and cessation of cambial activity, and thus radial growth throughout a growing season (e.g., see Begum et al., 2013; Rathgeber et al., 2016). Radial growth is increasingly considered to be limited by wood formation dynamics and their relation with environmental drivers, rather than solely by photosynthetic activity (Körner, 2015). In particular, the availability of soil water is critical for cell expansion (e.g., Peters et al., 2021) and most likely limits radial growth before photosynthesis (Fatichi et al., 2014); however, this water availability is again linked to local climate as higher temperatures drive evaporation and thus may contribute to the depletion of soil water storage, impeding growth.

Urban trees show a tendency for enhanced growth rates and/or productivity compared to rural conspecifics, which is typically attributed to increased temperatures (Jia et al., 2018; Pretzsch et al., 2017), yet feature a broad range of effect size ranges and signs (i.e., reduced growth) specific to species and location. Zhao et al. (2016) showed that productivity rates, as a proxy for growth, increased within urban clusters as urbanization intensifies using remotely sensed vegetation indices. Further, Moser-Reischl et al. (2019) identified positive associations between air temperature and radial growth for two species (total of 20 individuals) commonly selected by urban planners (T. cordata, Rubinia pseudoacacia) in Munich.

(Briber et al., 2015; O’Brien et al., 2012) … generally increased growth Contrastingly, Gillner et al. (2014) highlight decreased growth for Acer species (A. platanoides and pseudoplatanus), Platanus x hispanica and Quercus rubra with higher summer temperatures of the preceding year, especially when compounded with drought, in another German metropolis (Dresden). Quigley (2004) identified absolute growth potential decreased for species between rural and urban conspecifics, yet was limited to comparatively small sample sizes per group (\(n_{total}~=~230\) divided in 15 species, 3 groups and 2 locations) - also lacked multi-modal responses Pretzsch et al. (2017) inferred enhanced growth in recent decades and across urban locations spanning several latitudes, including Berlin - however, only 145 individuals of one species (T. cordata) were assessed there. As mentioned previously, climate-growth relationships can vary substantially between species, and in fact, Quigley (2004) and Pretzsch et al. (2017) report contrasting results regarding average tree diameter, i.e. smaller or larger for urban \(vs.\) rural trees of same age, consider other studies mentioned above Similarly, for Berlin, Dahlhausen et al. (2018), identified enhanced growth in highly urbanized environments (using basal area increments of 252 trees) for Tilia cordata Mill, the most abundant tree of the city, which they attributed to the UHI effect, while intermediate development intensity was adverse for tree growth.

These differences in growth trends may result from contrasting species-specific responses to increased temperatures, but are indeed affected by other (time-varying) factors and stochastic processes, such as water availability, pollution and road-salt loading, structural impedance by infrastructure, or management, etc. (Pauleit et al., 2002; Quigley, 2004; Randrup et al., 2001; Rhoades and Stipes, 1999). expand on location-specific factors that can affect growth This can hinder the extrapolation from individual sampling sites toward predicting effect across entire urban areas and tree stocks, especially where studies rely on labor-intensive methods which are limited logistically by sampling effort, reducing sample sizes, and species as well as spatial coverage. This is exacerbated by a lack of co-located environmental variables (i.e. measured in situ) at pertinent spatial scales, for instance, as noted by Wohlfahrt et al. (2019) for air temperature and tree leaf phenology, which may lead to incorrect inferences and interpretations for the role of climate change on growth/productivity when applying space-for-time substitutions.

Space-for-time substitutions are a common approach (cf. studies above) to generate inferences in observational (rather than treatment-control) studies, where manipulations are costly or logistically infeasible due to time and/or financial constraints.
However, they require accounting for confounding factors specific to trees’ environments, such as street characteristics, development intensity, available soil volume, etc. While several of the aforementioned studies applied the space-for-time approach to quantify temperature and excess heat on growth, they typically compare trees grouped using qualitative or summary descriptors of sampling sites, disregarding the spatio-temporal variability in location-specific factors noted above. This can hinder the extrapolation from individual sampling sites toward predicting effects across entire urban areas and tree stocks, especially when studies rely on labor-intensive methods which are limited logistically by sampling effort, reducing sample sizes, and species as well as spatial coverage. This can be exacerbated by a lack of co-located environmental variables (i.e. measured in situ) at pertinent spatial scales, for instance, as noted by Wohlfahrt et al. (2019) for air temperature and tree leaf phenology, which may lead to incorrect inferences and interpretations for the role of climate change on growth/productivity when applying space-for-time substitutions. It is thus likely that the varying and even contrasting growth responses observed for urban trees across and within studies is at least modulated by several confounding factors, making the attribution to a single driver, such as excess heat, more difficult and possibly less accurate.

These limitations could be overcome by relying on large data sets with extensive ancillary data coverage. Berlin, as one of the greenest cities in Europe, provides an openly accessible tree inventory, with spatio-temporal environmental data sets pertinent to tree growth, through its Environmental Agency. It features a total of 650000 individuals covering 94 genera and at least 600 species and/or cultivars, listing information on location, trunk diameter (at breast height; \(DBH\); see Tab.\(~\)1.1), and stem height, amongst other variables, for the majority of street and park trees. For this study, our object was to assess the impact of excess urban heat, i.e. the UHI effect, on tree growth using this openly available inventory data set, complemented by additional open data sources as well as incremental growth data from tree cores. The assessment relied on flexible statistical models that could capture species and location-specific responses to heat and other urban factors. Specifically, we aimed to (1) assess heat exposure of most abundant species; (2) determine the impact of (excess) heat on stem growth with space-for-time substitution to increase coverage; (3) h ighlight the role of location-specific environmental factors in mediating temperature responses. While this work constitutes a case study for Berlin, we believe the results are a valuable contribution toward Berlin’s current and future management of its tree stock. This is because the high temporal and spatial variability of controls on growth, and thus variability in responses, require that assessments are developed for a specific region, because well-understood tree characteristics (e.g., see Brune, 2016; Roloff et al., 2009), could be strongly modulated in predicable ways at a given location or time due to management, planting practices, or other environmental controls; for example, if drought hardiness is related to extensive root networks, small soil volumes available to street trees could render a species vulnerable to water stress. As such, the approach can also serve as a framework for base-line assessments for other cities with available or growing inventory and ancillary data [cite something on tree diversity in tree stocks, management, etc.], and also inform species-climate matrices regarding temperature sensitivity…..

OLD

Berlin features the most intense Urban Heat Island (UHI) in Germany due to its large extent and development intensity (Kuttler et al., 2015), with temperature increases of up to \(12~K\) during day-time and \(6~K\) on average for night-times (2001-2010, Fenner et al., 2014) in urban \(vs.\) rural areas. Consequently, urban green (infrastructure) systems are subjected to increased heat more frequently, potentially affecting their process dynamics - either positively or adversely. Their performance and health, however, is closely tied to local energy budgets (Grimmond et al., 1996 ; Hertel and Schlink, 2019), which in turn are decisive for controlling human wellbeing (e.g. Maras et al., 2016), amongst other factors. Assessing the effect of increased temperatures on green infrastructure, as part of the urban landscape, is therefore instrumental for understanding, and ultimately mitigating, the potential impact of future warming on increasingly urban societies (Norton et al., 2015).

Trees, in particular, provide shading as well as transpirative cooling in their vicinity (Endlicher et al., 2016; Gillner et al., 2015; Oke, 1982), and therefore can reduce ambient temperatures, infrastructure power-consumption and (human) thermal discomfort (Akbari et al., 2001; e.g. Gulyás et al., 2006; Hoyano, 1988; Mayer and Höppe, 1987); simultaneously, they provide numerous other environmental, cultural and psychological services and/or benefits (see Tzoulas et al., 2007 for review). Further, recent tree growth dynamics as a proxy for on-going and future warming may provide an additional line of evidence to support the growing knowledge base on future climate-vegetation dynamics (Zhao et al., 2016) and may aid in mitigation and adaptation efforts (Brune, 2016; Pretzsch et al., 2017).

Trees and green infrastructure in urban areas show a tendency for enhanced growth rates and/or productivity compared to rural counterparts (Jia et al., 2018; Pretzsch et al., 2017), yet feature a broad range of effect size ranges and, in some cases, signs specific to species and locality. Zhao et al. (2016) showed that growth rates increased within urban clusters as urbanization intensifies using remotely sensed vegetation indices. Similarly, for Berlin, Dahlhausen et al. (2018), identified positive growth modulation in highly urbanized environments (using growth increments) for Tilia cordata Mill, the most abundant tree of the city, which they attributed to the UHI effect, while intermediate development intensity showed indications of being least favorable for tree growth. Further, Moser-Reischl et al. (2019) identified positive associations between air temperature and radial growth for two species commonly selected by urban planners (T. cordata, Rubinia pseudoacacia) in Munich. By contrast, Gillner et al. (2014) highlight decreased growth for Acer species (A. platanoides and pseudoplatanus), Platanus x hispanica and Quercus rubra with higher summer temperatures of the preceding year, especially when compounded with drought, in another German metropolis (Dresden). Differences in growth trends may result from contrasting species-specific characteristics, but are indeed affected by other processes and factors, such as water availability, pollution and road-salt loading, structural impedance through infrastructure or management, etc. (Pauleit et al., 2002; Quigley, 2004; Randrup et al., 2001; Rhoades and Stipes, 1999). Under climate change, atmospheric drought will likely be compounded with high temperatures - and intensified UHIs - more frequently, adding further stress to current urban disturbance regimes (Roloff et al., 2009).

Conditions affecting tree growth can vary greatly within urban areas or regions, and need to be accounted for when establishing relationships with pertinent drivers, such as the UHI effect. This typically complicates the extrapolation from individual sampling sites toward predicting effect sizes across entire urban areas and tree stocks. This is especially the case for studies reliant on labour-intensive methods which are limited logistically by sampling effort, reducing sample sizes, as well as species and spatial coverage.

To complement (existing) detailed dendroecological analyses of climate-growth relationships in Berlin for key species, we propose inferring growth modulation from a large data set in excess of 650000 individuals covering 94 genera and at least 600 species and/or cultivars provided by the Berlin Senate Administration (Senatsverwaltung). This data set contains information on location, species, trunk diameter (at breast height; \(DBH\); see Tab.\(~\)1.1), and height, amongst other variables for the majority of street and park trees.

Table 1.1: Available records by category in entire data set (n), and those with age and \(DBH\) entries (n\(_{full}\)).
Category n n\(_{full}\)
Park 287423 172949
Street 370248 367608
Riparian 46364 0

In a space-for-time substitution, growth of individual species can be assessed across the entire city of Berlin, and related to effects of the UHI, while accounting for other location-specific factors, such as street characteristics, development intensity, available soil volume, etc. Comparable applications are found, for example, in Quigley (2004) and Pretzsch et al. (2017). The former inferred absolute growth potential for species across successional groups (early, mid, late stage), and between rural and urban conspecifics, yet lacked spatially-explicit effect size estimates across the urban-rural space and was limited to comparatively small sample sizes per group (\(n_{total}~=~230\) divided in 15 species, 3 groups and 2 locations). Pretzsch et al. (2017) applied linear hierarchical models to infer growth modulation on annual basis for different time periods and urban \(vs.\) rural locations while accounting for stand-level variability; however, for Berlin only 145 individuals of one species (T. cordata) were assessed. As mentioned previously, climate-growth relationships can vary substantially between species, and in fact, Quigley (2004) and Pretzsch et al. (2017) report contrasting results regarding average tree diameter, i.e. smaller or larger for urban \(vs.\) rural trees of same age. Consequently, this variability of effect sizes and directions calls for a more comprehensive assessment across species and with greater spatial coverage throughout Berlin.

We therefore propose applying a statistical model that is fully spatially explicit, while also allowing to account for the nested nature of the data set (e.g. streets and districts) as well as other pertinent factors using hierarchical, generalized additive models (see Section\(~\)2). As a result, the absolute growth potential of a species can be inferred given, for example, a specific location, age or UHI magnitude. Further, the impact of UHI loading can be predicted for a single species across all of Berlin as a continuous surface. The inclusion of independent, tree-level growth data, however, is paramount as it allows:

  1. validating the publicly-available Senate dataset (\(DBH\)) while providing a more reliable estimate of tree age,
  2. applying the model with annual basal area as a response (enabling incorporating effects of varying climate/UHI intensities over time), and
  3. comparing \(DBH\) (Senate data) and basal area-derived models for a subset of locations and species, increasing confidence in Berlin-wide predictions.

2 Methods

2.1 Study area

Berlin is one of the largest metropolitan areas in Central Europe (892\(~km^2\)) with a population of approximately 3.6 million, and a maximum extent of 38\(~km\) in North-South and 45\(~km\) in East-West directions. It is located in North-Eastern Germany, and lies in the temperate zone with warm-humid climate (Dfb) according to the updated Köppen-Geiger classification (Beck et al., 2018), with mean annual temperature of approximately 10\(^\circ C\) and precipitation of 575\(~mm\) (Tempelhof weather station, DWD). Berlin features low relief (approximately 30\(~m\) to 60\(~m\) with 120\(~m\) at solitary peaks), and is centered around a glacial outwash valley (sands, gravel), bordered by two plateaus consisting of glacial till and clay in the North-East and South, as well as sands in the South-West. The city provides extensive public green space covering around 30\(~\%\) of its area (SUVK, Berlin, 2019), with an extensive urban forest of nearly 700000 publically-managed trees along streets, in parks and in riparian areas. It has a pronounced urban heat island, owing to its high degree of built-up and sealed surfaces, with air temperatures up to 12\(^\circ C\) higher in urban compared to adjacent rural areas (Fenner et al., 2014).

2.2 Dendrochronological sampling and analyses

2.3 Statistical Analyses

2.3.1 Model development and selection

2.3.1.1 General approach: space-for-time analyses

2.3.1.2 Data sources

An overview of data used for models, including sources, types, and application, is provided in Table\(~\)??.

Trees
Characteristics of street trees and their respective environments were collated from the city’s tree inventory, as well as various elements of the Berlin Environment Atlas, which are openly available via https://daten.berlin.de and curated by the city’s government. The data used from the inventory includes species, location, age, and diameter at breast height (dbh).

Temperature/UHI data sets
Temperature and UHI data were summarized temporally either by the provider or manually to provide a characteristic representation of heat loading during summer at different times (morning, afternoon/day, night), from which tree averages (radius of 150\(~m\)) were calculated. Two data sets of urban air and one surface temperature were tested as explanatory variables in GAMM models. The air temperatures from the Berlin environmental atlas (EnvAt) were model outputs that are representations of typical summer conditions at 0400, 1400 and 2200 hours; these data are provided at city block basis (spatial polygons), from which weighted averages were extracted. UrbClim air temperatures are hourly model outputs (100\(~m\) resolution, ref) based on ERA5 re-analyses data (ECMWF) for which data of the hottest month in the record (June, 2011) were averaged to hours equivalent to EnvAt data by using a window of \(\pm~1~\)hour (i.e., 0300 to 0500, etc.). Subsequently, a land-use and landcover mask (2018, Copernicus CORINE ref) was used to define urban and rural/forested areas, by which the urban heat loading was calculated as \(UHI_{x,y} = T_{Air_{2m}~x,y} - \overline{T_{Air_{2m}~Rural}}\), where \(x\) and \(y\) define an urban grid cell. The surface UHI data set by Chakraborty and Lee (2019) derives its measure in a similar fashion and the reader is referred to the detailed description therein; note this data set provides day and night-time averaged UHI estimates at 500\(~m\) resolution, which were extracted for the hottest summer in this record (2007).

Ancillary data sets
Following the general approach described above, four ancillary dependent variables next to a temperature measure were employed in models; these were chosen due to their availability at high spatial resolution and coverage, and because their influence on growth was previously identified in literature or their likely impact could be deduced using ecophysiological principles. We included planting bed area, the sum of exchangeable basic cation as a proxy for soil nutrient availability, adjacent building height, and the proportional coverage of local climate zone 6 (LCZ6; open mid-rise, see Demuzere et al. (2019) and Stewart and Oke (2012) for details). The latter was chosen as an increase reflects a transition away from densely urbanized areas. Note that only street trees in urban, not rural areas or within greenspaces, were considered here, but individual trees may grow along streets adjacent to greenspaces and parks of varying sizes.

were considered to have The environment atlas also provided soil nutrient exchange capacity as a measure of growth-favoring soil conditions,

surface area of tree planting beds (“Baumscheibe”), as well as general characteristics of the urban environment like building height. It also includes spatially-explicit model outputs for local climate simulations representative of typical conditions, such as air temperature (2 m) on a 2015 summer’s day at different hours (0400, 1400, 2200). These model outputs were preferred over in situ measurements as more representative based on averaged conditions, physiologically more relevant than surface urban heat island products. These outputs are available at city block or planning unit level, and were used as a proxy for the general temperature distribution influenced by urbanization across the investigated growth period across the previous 80 years (see section X for details). This was deemed reasonable as Berlin’s built-up area has not changed markedly over the past 50 years, i.e., about 52 to 61\(\%\) (Mohamed, 2017). Further insight into the role of the urban environment was assessed by including local climate zone classes derived by WUDAPT. These describe the proportion of urban area with a specific cover, such as dense high rises, sealed surfaces, etc. For this study, the LCZ 6, representing dense mid-rise built up cover was used as a proxy for the degree of urbanization, and is the most frequent LCZ for Berlin (Fenner et al., 2017) (found ref in . Use percent sealed surface instead?

Table 2.1: Data description used for generating maps and route optimization. Resolution and radius are provided in \(m\), the latter referring to the buffer size across which data was averaged to estimate trees’ environmental conditions. A zero-radius refers to a point extraction from categorical and location specific data. Planting Bed Area, and Soil type are not currently used.
Name Accessed Type Unit Resolution Radius Source Reference
Street Trees Oct ’20 Point https://daten.berlin.de/
UHI Berlin Dec ’19 Raster \(^\circ C\) 500 150 https://yceo.yale.edu/research/global-surface-uhi-explorer Chakraborty et al. (2019)
UHI Berlin Dec ’19 Raster \(^\circ C\) 500 150 https://yceo.yale.edu/research/global-surface-uhi-explorer
Berlin Climate Model, Air temperature 2015 (Umweltatlas) Feb ’21 Polygon \(^\circ C\) 20 https://daten.berlin.de/
UrbClim ERA5 Model Output (ECMWF, UCSC) Mar ’21 Raster \(^\circ C\) 100 150 https://cds.climate.copernicus.eu/ Deridder et al. (2015)
Berlin Land-use Apr ’21 Polygon https://daten.berlin.de/
WUDAPT LCZ Oct ’20 Raster 100 150/300 https://www.wudapt.org/continental-lcz-maps/ Demuzere et al. (2019)
Berlin Veg/Building Height Oct ’20 Polygon \(m\) 150/300 https://daten.berlin.de/
Berlin Soil Nutrients, Bodenkundliche Kennwerte 2015 (Umweltatlas) Nov ’20 Polygon \(mol~m^{-2}\) 0 https://daten.berlin.de/
Planting Bed Area Oct ’20 Polygon \(m^2\) 0 https://daten.berlin.de/
Berlin Soils Oct ’20 Polygon 0 https://daten.berlin.de/
Berlin Districts Oct ’20 Polygon https://daten.berlin.de/
Berlin Transport Network Feb ’21 Polygon OpenStreetMap Overpass API
Berlin Water (Ways) Feb ’21 Polygon OpenStreetMap Overpass API

2.4 General analyses

The proposed statistical method is from the class of hierarchical, generalized additive models (GAM, or GAMM for mixed models/hierarchical models). In these models combinations of continuous and categorical predictor variables can be summed to estimate a response. In particular, continuous variables that are linearly, as well as non-linearly related to the response can be represented by applying a transfer function, typically termed “smoothing function” (Wood, 2017); these are constructed using a number of base functions of varying complexity and form, which provides a high degree of flexibility, ideal for fitting ecosystem dynamics which are rarely linear (Pedersen et al., 2019), or correctly represented with deterministic functional forms (e.g. quadratic equations). In general, a GAM can be written as:

\[\begin{equation} E (Y)~=~g^{-1}\left( \beta_0 + \sum_{i = 1}^{n} f_i (x_i) \right), \tag{2.1} \end{equation}\]

and

\[\begin{equation} y~=~E (Y) + \epsilon, \tag{2.2} \end{equation}\]

where \(Y\) is taken from an appropriate distribution and corresponding link function \(g\), \(\beta_0\) is the intercept and \(f_i\) represents a smooth function of a predictor (Pedersen et al., 2019), and \(\epsilon \sim \mathcal{N}(0, \sigma ^2)\). Note, that \(f_i\) consists of a smooth (e.g. spline) constructed via basis functions of different form and complexity, multiplied by a coefficient:

\[\begin{equation} f_i(x_i)~=~\sum_{k = 1}^{K} \beta_{i, k} b_{i,k}(x_i). \tag{2.3} \end{equation}\]

Nested data structures (e.g. due to similar road [type]) can be accounted for by introducing random effects (Wood, 2017), while spatial dependence between observations can be included by constructing smoothing functions with e.g. northings and eastings, as for example done in (Augustin et al., 2009). Ultimately, the implementation of a such a GAMM will allow for establishing continuous prediction surfaces of growth potential (approximated via \(DBH\)) for individual species across urban areas (including parks) of Berlin.

Currently, \(DBH\) has been modeled using a hierarchical linear model (linear mixed effects model) with lme4 (Bates et al., 2015) in R Core Team (2020) (see Section\(~\)3). The general form of this model is:

\[\begin{equation} Y_{i,j} = (\beta_0 + b_{0,i,j}) + (\beta_1 + b_{1,i,j}) \cdot x_i + \epsilon_{i,j}, \tag{2.4} \end{equation}\] where \(\beta_0\) is the intercept with its random component \(b_0\), and \(\beta_1\) the slope with its random component \(b_1\). The random errors are assumed i.i.d. and distributed as \(b \sim \mathcal{N}(0, \tau ^2)\). The model for which results are presented in Figure\(~\)3.5 estimates \(DBH\) from tree age and the local UHI intensity as continuous covariates with random slopes and intercepts for each species; note, that for computational efficiency each genera was modeled separately. Further, models were established for the three most abundant species per genera with at least 1000 individuals.

3 Preliminary results

Tree locations are clustered and structured based on their category, i.e. riparian, street and park trees (Fig.\(~\)3.1). Planting in space and time shows species-specific patterns (by districts), often related to major events, such as the start and end of armed and/or political conflict. Table\(~\)3.1 shows the binned distribution of genera across age classes.

Table 3.1: Binned age-distribution for trees in Berlin data set, and entries missing age information.
Genera (0,30] (30,60] (60,90] (90,120] (120,150] 150+ Total (n) Missing (n)
Tilia 43815 68818 39011 5647 315 198 168497 10693
Acer 34453 56397 16464 3239 214 126 149422 38529
Quercus 12358 21877 10315 4750 1075 1711 69202 17116
Betula 6325 11718 2236 135 4 1 29878 9459
Aesculus 5926 8993 6890 1929 207 43 27353 3365
Platanus 5084 12762 5473 1840 870 123 27117 965
Robinia 4812 9905 2491 413 38 9 25882 8214
Populus 1567 7824 3549 1189 227 110 20497 6031
Carpinus 7236 6123 1055 299 15 14 20172 5430
Prunus 7081 4126 365 32 5 0 18514 6905
Fraxinus 6266 5137 1203 260 22 5 17453 4560
Pinus 2144 4379 2317 446 24 5 16084 6769
Other 34839 24574 6547 3989 320 882 113964 42813
Marg. Totals 171906 242633 97916 24168 3336 3227 704035 160849
Individual tree locations for three categories available in Berlin Senate urban tree data set. Note, that for each category 7000 observations were subsampled from the available pool to facilitate visualization.

Figure 3.1: Individual tree locations for three categories available in Berlin Senate urban tree data set. Note, that for each category 7000 observations were subsampled from the available pool to facilitate visualization.

Gridded counts for the 11 most frequent genera, as well as *Pinus* and remaining genera. Note, that counts are standardized to unity for individual genera.

Figure 3.2: Gridded counts for the 11 most frequent genera, as well as Pinus and remaining genera. Note, that counts are standardized to unity for individual genera.

The distribution of the UHI effect is highly irregular and clustered in space (Fig.\(~\)3.3), and also shows variability through time (data not shown, refer to the urban heat island explorer).

Estimate of UHI intensity based on the algorithm in (Chakraborty and Lee, 2019), comparing urban with rural pixels within the greater metropolitan cluster. Presented values are averaged over the summer of 2007.

Figure 3.3: Estimate of UHI intensity based on the algorithm in (Chakraborty and Lee, 2019), comparing urban with rural pixels within the greater metropolitan cluster. Presented values are averaged over the summer of 2007.

The exposure to increased heat-loading of individual genera (and consequently species) is highly uneven throughout the city (Fig.\(~\)3.4). Street and park trees of most genera are clustered in urban areas with intermediate to high UHI loading, while riparian trees, and some street and park trees of other genera tend to be spread more evenly across Berlin’s UHI range.

Empirical density distribution of all individuals within the presented genera along the UHI continuum. UHI intensities were extracted for each tree location, and the distribution hence represents the first detailed overview of the exposure of Berlin's trees to urban heat loading. The black line is the density across all three categories. Insets show corresponding tree totals.

Figure 3.4: Empirical density distribution of all individuals within the presented genera along the UHI continuum. UHI intensities were extracted for each tree location, and the distribution hence represents the first detailed overview of the exposure of Berlin’s trees to urban heat loading. The black line is the density across all three categories. Insets show corresponding tree totals.

Note, that results below are preliminary and should be considered as a template for future outputs, rather than used for inference. The effect of UHI loading on absolute growth potential varies between genera and species (Fig.\(~\)3.5). Most notably, Quercus, the 3rd-most frequent genera, shows decreased absolute growth with increasing UHI loading, while the most frequent genera, Tilia, features contrasting relationships between species. The estimated effect sizes presented here are linear. However, temperature may exert a non-linear control on absolute growth and, hence, applying a method able to capture such dynamics may result in somewhat different effect sizes / behavior. Additionally, if temperatures increase in the future under climate warming, any non-linear effects may become more enhanced, stressing the need for a more flexible model fit and structure (i.e. using GAMM over linear models-).

Impact of UHI loading on tree diameter (\(DBH\)), accounting for age and inter-specific differences from the linear mixed model (via random slopes and intercepts). Line-ranges are standard errors of predicted effect sizes (i.e. slopes). Differences between street and park trees are considerable for some species, and may be due to local clustering and/or spatial under-representation across the UHI continuum. Further investigations need to address the degree of spatial autocorrelation and account for it where required in linear mixed models, and with smoothing interactions in a GAMM implementation.

Figure 3.5: Impact of UHI loading on tree diameter (\(DBH\)), accounting for age and inter-specific differences from the linear mixed model (via random slopes and intercepts). Line-ranges are standard errors of predicted effect sizes (i.e. slopes). Differences between street and park trees are considerable for some species, and may be due to local clustering and/or spatial under-representation across the UHI continuum. Further investigations need to address the degree of spatial autocorrelation and account for it where required in linear mixed models, and with smoothing interactions in a GAMM implementation.

4 Discussion

  1. Temperature, environmental and urban controls on tree growth

    • Intra specific differences
      • management
      • root vs. canopy (huber value?)
      • comparison young vs. old -> increased CO2, perhaps limitation of space for time, as lower conductance under high CO2 may result in more water savings (check WUE in old vs. young trees? future direction).(Dusenge et al., 2019) (McCarthy et al., 2011)
    • Sensitive trees in hot spots
    • Temporal dynamics
    • Validity and limitations

    (Bussotti et al., 2014)

  2. Implications:

5 Outlook

We seek to build upon and improve the current analysis by:

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6.0.1 Colophon

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#> [1] /home/hurley/_work/renv/berlin.trees-c2f6692a/R-4.1/x86_64-pc-linux-gnu
#> [2] /tmp/Rtmpt7UINb/renv-system-library
#> [3] /tmp/RtmpdSFlZn/renv-system-library
#> 
#>  P ── Loaded and on-disk path mismatch.

The current Git commit details are:

#> Local:    master /home/hurley/_work/p_024_GFZ_berlin_trees/berlin.trees
#> Remote:   master @ origin (https://github.com/the-Hull/berlin.trees)
#> Head:     [61803c0] 2021-10-22: added SI temp comparison